Geometry of the Space of Sections of Twistor Spaces with Circle Action
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866912869097930752 |
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| author | Beck, Florian Biswas, Indranil Heller, Sebastian Röser, Markus |
| author_facet | Beck, Florian Biswas, Indranil Heller, Sebastian Röser, Markus |
| contents | We study the holomorphic symplectic geometry of (the smooth locus of) the space of holomorphic sections of a twistor space with rotating circle action. The twistor space carries a line bundle with meromorphic connection constructed by Hitchin. We give an interpretation of Hitchin's meromorphic connection in the context of the Atiyah-Ward transform of the corresponding hyperholomorphic line bundle. It is shown that the residue of the meromorphic connection serves as a moment map for the induced circle action, and furthermore the critical points of this moment map are studied. Particular emphasis is given to the example of Deligne-Hitchin moduli spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_10853 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Geometry of the Space of Sections of Twistor Spaces with Circle Action Beck, Florian Biswas, Indranil Heller, Sebastian Röser, Markus Differential Geometry 53C26, 53C28, 53C43, 14H60, 14H70 We study the holomorphic symplectic geometry of (the smooth locus of) the space of holomorphic sections of a twistor space with rotating circle action. The twistor space carries a line bundle with meromorphic connection constructed by Hitchin. We give an interpretation of Hitchin's meromorphic connection in the context of the Atiyah-Ward transform of the corresponding hyperholomorphic line bundle. It is shown that the residue of the meromorphic connection serves as a moment map for the induced circle action, and furthermore the critical points of this moment map are studied. Particular emphasis is given to the example of Deligne-Hitchin moduli spaces. |
| title | Geometry of the Space of Sections of Twistor Spaces with Circle Action |
| topic | Differential Geometry 53C26, 53C28, 53C43, 14H60, 14H70 |
| url | https://arxiv.org/abs/2102.10853 |